Solve the following differential equation: `x y(dy)/(dx)=1+x+y+x y`

Explanation

`x y frac{d y}{d x}+1+x+y+x y=0`



`Rightarrow x y frac{d y}{d x}+(1+x)(1+y)=0`



`Rightarrow(frac{y}{1+y}) d y+(frac{1+x}{x}) d x=0`



`Rightarrow(1-frac{1}{1+y}) d y+(1+frac{1}{x}) d x=0`



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